President Abbas condemned the attack on a Palestinian refugee camp in Syria on Thursday which killed at least 20 people and wounded 65, a statement from his office said.
Witnesses in Yarmouk camp told Reuters by telephone that mortars hit a busy street as people were preparing a Ramadan meal to break their fasting.
"I saw it all, I was going to my house when the first round hit the street, people ran to check the damage when the second one hit the same area," a resident said.
"Many people were killed immediately," she said.
Doctors at three nearby hospitals said at least 20 people were killed and 65 wounded.
Yarmouk camp is the largest Palestinian refugee community and is home to more than 100,000 people.
It was not immediately clear what prompted the shelling.
President Abbas' office stressed that the Palestinian position towards Syria was not to interfere in Syrian internal affairs, and that refugee camps in the country would remain neutral.
The office of the presidency called for an end to violence in refugee camps.
Last week, forces loyal to Syrian President Bashar Assad bombed a hospital in Damascus' Yarmouk refugee camp, Palestinian sources had told Ma'an.
The Syrian army was targeting the hospital because medics were treating wounded from all sides, while Assad's regime only allowed its own soldiers to be treated, sources said.
A Red Crescent medical complex also suffered widespread damage from shelling. There is now only one functioning hospital in Yarmouk camp.
The following day, forces loyal to Syrian President Bashar Assad detained injured patients from the Palestine Hospital in Damascus, taking them to an unknown destination, sources said.
Syrian President Bashar Assad is trying to crush a 17-month revolt against his rule in which more than 18,000 people have been killed.